The Sommerfeld enhancement factor via a light scalar mediator is given
by the wavefunction, which will be defined soon in
Eq. (REF ) (see Ref. [1]} for a
review). The wavefunction obeys the following Schrödinger
equation where the potential is given by the Yukawa type,
\(\frac{1}{m_{\rm dm}}\frac{d^2\psi (r)}{dr^2}-V(r)\psi (r)= -m_{\rm dm}v^2\psi (r)\,,\) 
